6.19.19 problem section 9.3, problem 19

Internal problem ID [2166]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 19
Date solved : Tuesday, September 30, 2025 at 05:24:32 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-5 y^{\prime }-2 y&=18 \,{\mathrm e}^{x} \left (5+2 x \right ) \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 34

ode:=2*diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(diff(y(x),x),x),x)-5*diff(y(x),x)-2*y(x) = 18*exp(x)*(5+2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_4 \,{\mathrm e}^{-\frac {x}{2}}+c_2 \,{\mathrm e}^{-2 x}+c_3 \,{\mathrm e}^{-x}+{\mathrm e}^{x} \left (x^{2}+c_1 +2 x \right ) \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 48

ode=2*D[y[x],{x,4}]+5*D[y[x],{x,3}]+0*D[y[x],{x,2}]-5*D[y[x],x]-2*y[x]==18*Exp[x]*(5+2*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (e^{3 x} \left (x^2+2 x-\frac {40}{9}+c_4\right )+c_1 e^{3 x/2}+c_3 e^x+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.205 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-36*x - 90)*exp(x) - 2*y(x) - 5*Derivative(y(x), x) + 5*Derivative(y(x), (x, 3)) + 2*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{- 2 x} + C_{3} e^{- x} + C_{4} e^{- \frac {x}{2}} + \left (C_{1} + x^{2} + 2 x\right ) e^{x} \]